Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Richard Polt and Geoffrey Hellman

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8 ideas

1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
Knowledge is not a static set of correct propositions, but a continuing search for better interpretations [Polt]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]
10. Modality / B. Possibility / 1. Possibility
When we consider possibilities, there must be something we are considering [Polt]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]